Dynamics of social processes in populations, such as the spread of emotions, influence, language, mass movements, and warfare (often referred to individually and collectively as contagions), are increasingly studied because of their social, political, and economic impacts. Discrete dynamical systems (discrete in time and discrete in agent states) are often used to quantify contagion propagation in populations that are cast as graphs, where vertices represent agents and edges represent agent interactions. We refer to such formulations as graph dynamical systems. For social applications, threshold models are used extensively for agent state transition rules (i.e., for vertex functions). In its simplest form, each agent can be in one of two states (state 0 (1) means that an agent does not (does) possess a contagion), and an agent contracts a contagion if at least a threshold number of its distance-1 neighbors already possess it. The transition to state 0 is not permitted. In this study, we extend threshold models in three ways. First, we allow transitions to states 0 and 1, and we study the long-term dynamics of these bithreshold systems, wherein there are two distinct thresholds for each vertex; one governing each of the transitions to states 0 and 1. Second, we extend the model from a binary vertex state set to an arbitrary number r of states, and allow transitions between every pair of states. Third, we analyze a recent hierarchical model from the literature where inputs to vertex functions take into account subgraphs induced on the distance-1 neighbors of a vertex. We state, prove, and analyze conditions characterizing long-term dynamics of all of these models. / Master of Science

Dynamics of social processes in populations, such as the spread of emotions, influence, opinions, and mass movements (often referred to individually and collectively as contagions), are increasingly studied because of their economic, social, and political impacts. Moreover, multiple contagions may interact and hence studying their simultaneous evolution is important. Within the context of social media, large datasets involving many tens of millions of people are leading to new insights into human behavior, and these datasets continue to grow in size. Through social media, contagions can readily cross national boundaries, as evidenced by the 2011 Arab Spring. These and other observations guide our work. Our goal is to study contagion processes at scale with an approach that permits intricate descriptions of interactions among members of a population. Our contributions are a modeling environment to perform these computations and a set of approaches to predict contagion spread size and to block the spread of contagions. Since we represent populations as networks, we also provide insights into network structure effects, and present and analyze a new model of contagion dynamics that represents a person\'s behavior in repeatedly joining and withdrawing from collective action. We study variants of problems for different classes of social contagions, including those known as simple and complex contagions. / Ph. D.

Network science emerged as an interdisciplinary field over the last 20 years, and played a central role to address fundamental problems in other fields, e.g., epidemiology, public health, and transportation, and is now part of most university curriculums. Network dynamics is a major area within network science where researchers study different forms of processes in networked populations, such as the spread of emotions, influence, opinions, flu, ebola, and mass movements. These processes often referred to individually and collectively as contagions. Contagions are increasingly studied because of their economic, social, and political impacts. Yet, resources for studying network dynamics are largely dispersed and stand-alone. Furthermore, many researchers interested in the study of networks are not computer scientists. As a result, they do not have easy access to computing and data resources. Even with the presence of software or tools, it is challenging to install, build, and maintain software. These challenges create a barrier for researchers and domain scientists. The goal of this work is the design and implementation of a research framework for modeling contagions on large networked populations. The framework consists of various systems and services that provide support for researchers and domain scientists at different stages of their research workflow. / Ph. D.